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Harnack inequality for nondivergent linear elliptic operators on Riemannian manifolds : a self-contained proof Mun, Byeongju


In this paper, a self-contained proof is given to a well-known Harnack inequality of second order nondivergent uniformly elliptic operators on Riemannian manifolds with the condition that M-[R(v )]>0, following the ideas of M. Safonov [5]. Basically, the proof consists of three parts: 1) Critical Density Lemma, 2) Power-Decay of the Distribution Functions of Solutions, and 3)Harnack Inequality.

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